# Parsimonious mixtures of multivariate contaminated normal distributions

arXiv: https://arxiv.org/abs/1305.4669 · HTML: https://mlsanity.com/paper/1305.4669/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2013.

## Built on by (most cited first, 8 of 8)

- [Outlier detection in multivariate functional data through a contaminated mixture model](https://mlsanity.com/paper/2106.07222/) (2021)
- [Vine copula mixture models and clustering for non-Gaussian data](https://mlsanity.com/paper/2102.03257/) (2021)
- [Unsupervised Outlier Detection using Random Subspace and Subsampling Ensembles of Dirichlet Process Mixtures](https://mlsanity.com/paper/2401.00773/) (2024)
- [Adaptively Robust and Sparse K-means Clustering](https://mlsanity.com/paper/2407.06945/) (2024)
- [A Non-Parametric Bootstrap for Spectral Clustering](https://mlsanity.com/paper/2209.05812/) (2022)
- [Clustering Three-Way Data with Outliers](https://mlsanity.com/paper/2310.05288/) (2023)
- [Heckman Selection Contaminated Normal Model](https://mlsanity.com/paper/2409.12348/) (2024)
- [Robust model-based clustering via mixtures of multivariate pseudo-Voigt distributions](https://mlsanity.com/paper/2608.27606/) (2026)

## Abstract (arXiv)

A mixture of multivariate contaminated normal distributions is developed for model-based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild outliers and one specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori, adding a flexibility to our approach. Parsimony is introduced via eigen-decomposition of the component covariance matrices, and sufficient conditions for the identifiability of all the members of the resulting family are provided. An expectation-conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. Using a large scale simulation study, the behaviour of the proposed approach is investigated and comparison with well-established finite mixtures is provided. The performance of this novel family of models is also illustrated on artificial and real data.